forked from eggy/eifueo
159 lines
6.6 KiB
Markdown
159 lines
6.6 KiB
Markdown
# SL Physics
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The course code for this page is **SPH3U7**.
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## 1.1 - Measurements in physics
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### Fundamental units
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Every other SI unit is derived from the fundamental SI units. Memorise these!
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| Quantity type | Unit | Symbol |
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| --- | --- | --- |
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| Time | Second | s |
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| Distance | Metre | m |
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| Mass | Kilogram | kg |
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| Electric current | Ampere | A |
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| Temperature | Kelvin | K |
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| Amount of substance | Mole | mol |
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| Luminous intensity | Candela | cd |
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### Metric prefixes
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Every SI unit can be expanded with metric prefixes.
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!!! example
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milli + metre = millimetre ($10^{-3}$) m
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| Prefix | Abbreviation | Value | Inverse ($10^{-n}$) abbreviation | Inverse prefix |
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| --- | --- | --- | --- | --- |
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| deca- | da | $10^1$ | d | deci- |
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| hecto- | h | $10^2$ | c | centi- |
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| kilo- | k | $10^3$ | m | milli- |
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| mega- | M | $10^6$ | µ | micro- |
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| giga- | G | $10^9$ | n | nano- |
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| tera- | T | $10^{12}$ | p | pico- |
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| peta- | P | $10^{15}$ | f | femto- |
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| exa- | E | $10^{18}$ | a | atto- |
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### Significant figures
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- The leftmost non-zero digit is the **most significant digit**.
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- If there is no decimal point, the rightmost non-zero digit is the **least significant digit**.
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- Otherwise, the right-most digit (including zeroes) is the least significant digit.
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- All digits between the most and least significant digits are significant.
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- Pure (discrete) numbers are unitless and have infinite significant figures.
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!!! example
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In $123000$, there are 3 significant digits.<br>
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In $0.1230$, there are 4 significant digits.
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- When adding or subtracting significant figures, the answer has the **same number of decimals** as the number with the lowest number of decimal points.
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- When multiplying or dividing significant figures, the answer has the **same number of significant figures** as the number with the lowest number of significant figures.
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- Values of a calculated result can be **no more precise** than the least precise value used.
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!!! example
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$$1.25 + 1.20 = 2.45$$
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$$1.24 + 1.2 = 2.4$$
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$$1.2 × 2 = 2$$
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$$1.2 × 2.0 = 2.4$$
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!!! warning
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When rounding an answer with significant figures, if the **least significant figure** is $5$, round up only if the **second-least** significant figure is **odd**.
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$$1.25 + 1.2 = 2.4$$
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$$1.35 + 1.2 = 2.6$$
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### Scientific notation
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Scientific notation is written in the form of $m×10^{n}$, where $1 \leq m < 10, n \in \mathbb{Z}$. All digits before the multiplication sign in scientific notation are significant.<br>
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!!! example
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The speed of light is 300 000 000 ms<sup>-1</sup>, or $3×10^8$ ms<sup>-1</sup>.
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### Orders of magnitude
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The order of magnitude of a number can be found by converting it to scientific notation and taking its power of 10.
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!!! example
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- The order of magnitude of $212000$, or $2.12×10^{5}$, is 5.
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- The order of magnitude of $0.212$, or $2.12×10^{-1}$, is -1.
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## 1.2 - Uncertainties and errors
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### Random and systematic errors
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| Random error | Systematic error |
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| --- | --- |
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| Caused by imperfect measurements and is present in every measurement. | Caused by a flaw in experiment design or in the procedure. |
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| Can be reduced (but not avoided) by repeated trials or measurements. | Cannot be reduced by repeated measurements, but can be avoided completely. |
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| Error in precision. | Error in accuracy. |
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!!! example
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- The failure to account for fluid evaporating at high temperatures is a systematic error, as it cannot be minimised by repeated measurements.
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- The addition of slightly more solute due to uncertainty in instrument data is a random error, as it can be reduced by averaging the result of multiple trials.
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<img src="/resources/images/types-of-error.png" width=700>(Source: Kognity)</img>
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### Uncertainties
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Uncertainties are stated in the form of [value] ± [uncertainty]. A value is only as precise as its absolute uncertainty. Absolute uncertainty of **measurement** is usually represented to only 1 significant digit.
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!!! note
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Variables with uncertainty use an uppercase delta for their uncertainty value: $a ± \Delta a$
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- The absolute uncertainty of a number is written in the same unit as the value.
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- The percentage uncertainty of a number is the written as a percentage of the value.
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!!! example
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- Absolute uncertainty: 1.0 g ± 0.1 g
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- Percentage uncertainty: 1.0 g ± 10%
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To determine a measurement's absolute uncertainty, if:
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- the instrument states its uncertainty, use that.
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- an analog instrument is used, the last digit is estimated and appended to the end of the reported value. The estimated digit is uncertain by 5 at its order of magnitude.
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- a digital instrument is used, the last reported digit is uncertain by 1 at its order of magnitude.
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!!! example
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- A ruler has millimetre markings. A pencil placed alongside the ruler has its tip just past 14 mm but before 15 mm. The pencil is 14.5 mm ± 0.5 mm long.
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- A digital scale reads 0.66 kg for the mass of a human body. The human body has a mass of 0.66 kg ± 0.01 kg.
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!!! info
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See [Dealing with Uncertainties](/resources/g11/physics-uncertainties.pdf) for how to perform operations with uncertainties.
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### Error bars
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Error bars represent the uncertainty of the data, typically representing that data point's standard deviation, and can be both horizontal or vertical.
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<img src="/resources/images/error-bars.png" width=600>(Source: Kognity)</img>
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!!! note
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On a graph, a data point with uncertain values is written as $(x ± \Delta x, y ± \Delta y)$
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### Uncertainty of gradient and intercepts
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!!! note "Definition"
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- The **line of best fit** is the line that passes through **all error bars** while passing as closely as possible to all data points.
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- The **minimum and maximum lines** are lines that minimise/maximise their slopes while still passing through **all error bars.**
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!!! warning
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- Use solid lines for lines representing **continuous data** and dotted lines for **discrete data**.
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<img src="/resources/images/error-slopes.png" width=700>(Source: Kognity)</img>
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The uncertainty of the **slope** of the line of best fit is the difference between the maximum and minimum slopes.
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$$m_{best fit} ± m_{max}-m_{min}$$
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The uncertainty of the **intercepts** is the difference between the intercepts of the maximum and minimum lines.
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$$intercept_{best fit} ± intercept_{max} - intercept_{min}$$
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## 1.3 - Vectors and scalars
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## Resources
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- [IB SL Physics Syllabus](/resources/g11/ib-physics-syllabus.pdf)
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- [Dealing with Uncertainties](/resources/g11/physics-uncertainties.pdf)
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- [Linearising Data](/resources/g11/linearising-data.pdf)
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- [External: IB Physics Notes](https://ibphysics.org)
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